Best Known (48, 48+6, s)-Nets in Base 7
(48, 48+6, 5592402)-Net over F7 — Constructive and digital
Digital (48, 54, 5592402)-net over F7, using
- 72 times duplication [i] based on digital (46, 52, 5592402)-net over F7, using
- trace code for nets [i] based on digital (20, 26, 2796201)-net over F49, using
- net defined by OOA [i] based on linear OOA(4926, 2796201, F49, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(4926, large, F49, 6) (dual of [large, large−26, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 25679568 | 495−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(4926, large, F49, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(4926, 2796201, F49, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- trace code for nets [i] based on digital (20, 26, 2796201)-net over F49, using
(48, 48+6, large)-Net over F7 — Digital
Digital (48, 54, large)-net over F7, using
- t-expansion [i] based on digital (47, 54, large)-net over F7, using
- 1 times m-reduction [i] based on digital (47, 55, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(755, large, F7, 8) (dual of [large, large−55, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 20176803 | 79−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(755, large, F7, 8) (dual of [large, large−55, 9]-code), using
- 1 times m-reduction [i] based on digital (47, 55, large)-net over F7, using
(48, 48+6, large)-Net in Base 7 — Upper bound on s
There is no (48, 54, large)-net in base 7, because
- 4 times m-reduction [i] would yield (48, 50, large)-net in base 7, but